Number of digits in the n’th Fibonacci Number

Number of digits in the n’th Fibonacci Number.

Given a number n, find the number of digits in the n’th Fibonacci Number.

Example: n = 1000, then Fibonacci number is "43466557686937456435688527675040625802564660517371780402481729089536555417949051890403879840079255169295922593080322634775209689623239873322471161642996440906533187938298969649928516003704476137795166849228875"
and number of digit is 209

Code should be optimize enough to calculate 1000th number in Fibonacci series.